MAT 102 - Calculus II

Syllabus for MAT 102 – Calculus II

This is a compulsory course for BS Mathematics students in their 3^rd semester.

Credits (Lec:Tut:Lab)= 3:1:0 (3 lectures and 1 tutorial weekly)

Prerequisites: MAT 101 (Calculus I) or equivalent

Brief Description: The first part deals with series of numbers and functions. The second part is an introduction to multivariable calculus, finishing with the various versions of Stokes' theorem. The concepts and techniques covered here are used extensively in the social and natural sciences as well as in engineering to study systems with many dimensions.

Detailed Syllabus:

1. Sequences and Series: Limits of sequences, algebra of limits, series, divergence test, comparison and limit comparison tests, integral test, alternating series test, absolute convergence, root & ratio tests, power series, Taylor series

2. Vectors: Dot and cross product, equations of lines and planes, quadric surfaces, space curves, arc length and curvature

3. Differential calculus in several variables: Functions of several variables, level curves and surfaces, limits and continuity, partial derivatives, tangent planes, chain rule, directional derivatives, gradient, Lagrange multipliers, extreme values and saddle points, 2^nd derivative test

4. Double and triple integrals: Double integrals over rectangles, double integrals over general regions, double integrals in polar coordinates, center of mass, triple integrals, triple integrals in cylindrical coordinates, triple integrals in spherical coordinates, change of variables

5. Vector Integration: Vector fields, line integrals, fundamental theorem, independence of path, Green's theorem, divergence, curl, parametric surfaces, area of a parametric surface, surface integrals, Stokes' theorem, Gauss' divergence theorem

Main Reference:

• Essential Calculus – Early Transcendentals, by James Stewart. Cengage, India Edition.

Supplementary References:

• Calculus and Analytic Geometry by G B Thomas and R L Finney, 9^th edition, Pearson.
• Basic Multivariable Calculus by J E Marsden, A J Tromba and A Weinstein, 1^st edition, Springer (India), 2011.
• Calculus by Ken Binmore and Joan Davies, 1^st edition, Cambridge, 2010.